Stats 2 tips‎ > ‎

### F test notes

posted Dec 3, 2010, 7:07 PM by Prof Kiernan   [ updated Dec 3, 2010, 7:39 PM ]
 You can use the F test to verify a claim about a standard deviation (or variance) for 2 data sets. Assumptions: The sample is from a "normal distribution" NOTE: some professors prefer to use the following notation: N~(mean, Standard Deviation) English Translation: Use an F test  if you are Given: 2 sample sizes (n) and 2 standard deviations (or variances=s2 ) AND you are testing a claim about a standard deviation or variance. Writing the hypothesis: H0:  population standard deviation1 = population standard deviation2 H1: population standard deviation1  is less than, greater than, or not equal to population standard deviation2 Critical Value = shaded area from F table using the degrees of freedom.Degrees of freedom: for numerator (use the info from the bigger Standard Deviation) n-1, for denominator (use the info from the smaller Standard Deviation) n-1. Remember that if the null hypothesis requires two tails, split the alpha before using the tables. Test statistic formula: F = variance1 / variance2 **The bigger variance (standard deviation squared) must be divided by the smaller variance (standard deviation squared).** Calculator: Press STAT Highlight TESTS Select 2-SampFTest  Put your information in.    **NOTE: S1 must be the biggest standard deviation**Make sure the not equal to, less than, or greater than symbol matches the one in your alternative hypothesis (H1).Highlight Calculate Press ENTERF is the test statistic, and P is the P-value.Rejection of the null hypothesis (Ho):You can reject the null hypothesis if:the F from the formula falls in the shaded critical area from the table.the P-value is smaller than your alpha Reject Ho. Remember: if you are not given an alpha assume you are using 0.05.